{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import division, print_function\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Morphological operations\n",
    "\n",
    "Morphology is the study of shapes. In image processing, some simple operations can get you a long way. The first things to learn are *erosion* and *dilation*. In erosion, we look at a pixel’s local neighborhood and replace the value of that pixel with the minimum value of that neighborhood. In dilation, we instead choose the maximum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from matplotlib import pyplot as plt, cm\n",
    "import skdemo\n",
    "plt.rcParams['image.cmap'] = 'cubehelix'\n",
    "plt.rcParams['image.interpolation'] = 'none'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x107af2510>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107a49ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "image = np.array([[0, 0, 0, 0, 0, 0, 0],\n",
    "                  [0, 0, 0, 0, 0, 0, 0],\n",
    "                  [0, 0, 1, 1, 1, 0, 0],\n",
    "                  [0, 0, 1, 1, 1, 0, 0],\n",
    "                  [0, 0, 1, 1, 1, 0, 0],\n",
    "                  [0, 0, 0, 0, 0, 0, 0],\n",
    "                  [0, 0, 0, 0, 0, 0, 0]], dtype=np.uint8)\n",
    "plt.imshow(image)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The documentation for scikit-image's morphology module is\n",
    "[here](http://scikit-image.org/docs/0.10.x/api/skimage.morphology.html).\n",
    "\n",
    "Importantly, we must use a *structuring element*, which defines the local\n",
    "neighborhood of each pixel. To get every neighbor (up, down, left, right, and\n",
    "diagonals), use `morphology.square`; to avoid diagonals, use\n",
    "`morphology.diamond`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107b4f610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from skimage import morphology\n",
    "sq = morphology.square(width=3)\n",
    "dia = morphology.diamond(radius=1)\n",
    "disk = morphology.disk(radius=30)\n",
    "skdemo.imshow_all(sq, dia, disk)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The central value of the structuring element represents the pixel being considered, and the surrounding values are the neighbors: a 1 value means that pixel counts as a neighbor, while a 0 value does not. So:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10934d7d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "skdemo.imshow_all(image, morphology.erosion(image, sq), shape=(1, 2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1097865d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "skdemo.imshow_all(image, morphology.dilation(image, sq))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "and"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "3Cgnhvw6mvyaboT8qjEz7FTl16va3JFwb/XnC89Sm7b+YPV/ba4XeMOy4/SSNod772pziPXONrcB\n",
       "L+U32pzXvavNLZtvWXCWx7q55e/eeGabdXNXm1uQR9imq57TZk/rP6u/zd1nc5FfFya/phshv2rM\n",
       "DJNfAAAAAAAAAAAAAAAAAAAAAAAAAABL+3+tgMTY7N49HQAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109208d90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "skdemo.imshow_all(image, morphology.dilation(image, dia))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Erosion and dilation can be combined into two slightly more sophisticated operations, *opening* and *closing*. Here's an example:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1092503d0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "BnwArOlolsuBO0m/uEZI/0Z9P/+oi0AOk54cnzSPtBfpygzgceAhYHNHMywBVgKvkU4xWA5s6GCO\n",
       "Q9Xt+er+RlIoXbiKdKrFW6SHeptI/58G3nTgVdJvhpl0+yR9iPSDuK6j738my+j2KNazwMLq4x8B\n",
       "P+lojsWkI4sXk/6d1gPf6miWvvsS6YjRfrq9bNDnSY/5d5Ie3uzgo5c56rdldHsUazFpD1LCdc++\n",
       "z6nDvOtJe3tJkiRJkiRJkiRJatf/AF5uSA5B4jrdAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109301450>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "image = np.array([[0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "                  [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "                  [0, 0, 1, 1, 1, 1, 1, 1, 0, 0],\n",
    "                  [0, 0, 1, 1, 1, 1, 1, 1, 0, 0],\n",
    "                  [0, 0, 1, 1, 1, 1, 1, 1, 0, 0],\n",
    "                  [0, 0, 1, 1, 1, 0, 0, 1, 0, 0],\n",
    "                  [0, 0, 1, 1, 1, 0, 0, 1, 0, 0],\n",
    "                  [0, 0, 1, 1, 1, 0, 0, 1, 0, 0],\n",
    "                  [0, 0, 1, 1, 1, 1, 1, 1, 0, 0],\n",
    "                  [0, 0, 1, 1, 1, 1, 1, 1, 0, 0],\n",
    "                  [0, 0, 1, 1, 1, 1, 1, 1, 0, 0],\n",
    "                  [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],\n",
    "                  [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], np.uint8)\n",
    "plt.imshow(image)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What happens when run an erosion followed by a dilation of this image?\n",
    "\n",
    "What about the reverse?\n",
    "\n",
    "Try to imagine the operations in your head before trying them out below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107b39a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "skdemo.imshow_all(image, morphology.opening(image, sq)) # erosion -> dilation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": [
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       "un4AAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109173690>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "skdemo.imshow_all(image, morphology.closing(image, sq)) # dilation -> erosion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**: use morphological operations to remove noise from a binary image."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1092624d0>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "/pgfhw/ZPQXRCKs+5oiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiI7cT/AUCPe054\n",
       "QlRvAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1091c48d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from skimage import data, color\n",
    "hub = color.rgb2gray(data.hubble_deep_field()[350:450, 90:190])\n",
    "plt.imshow(hub)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Remove the smaller objects to retrieve the large galaxy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/nuneziglesiasj/anaconda/lib/python2.7/site-packages/scikit_image-0.11dev-py2.7-macosx-10.5-x86_64.egg/skimage/util/dtype.py:107: UserWarning: Possible precision loss when converting from float64 to uint8\n",
      "  \"%s to %s\" % (dtypeobj_in, dtypeobj))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(<matplotlib.axes.AxesSubplot at 0x1096b59d0>,\n",
       " <matplotlib.axes.AxesSubplot at 0x109358b10>)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "QmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1092cf390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "iIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIhIlv1/MvmjHuGbpcwAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1096c6cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "disk = morphology.disk(radius=8)\n",
    "gal = morphology.opening(hub, disk)\n",
    "plt.imshow(gal)\n",
    "skdemo.imshow_with_histogram(gal)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10930c0d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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       "GFf4BeHb4bWsfb8/RXgODxEamJIkSZIkSZIkSZIkSZIkSZIkSZImyf8Dk1ncNonv3RkAAAAASUVO\n",
       "RK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10930c950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "gal_selector = gal > 50\n",
    "# use numpy boolean indexing to estimate histogram\n",
    "# of brightness intensity on isolated galaxy\n",
    "skdemo.imshow_all(hub, gal_selector)\n",
    "f = plt.figure()\n",
    "plt.hist(hub[gal_selector], bins=50);"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
